The iterative solver template library. The numerical solution of partial differential equations frequently requires the solution of large and sparse linear systems. Using generic programming techniques in C++ one can create solver libraries that allow efficient realization of “fine grained interfaces”, i.e. with functions consisting only of a few lines, like access to individual matrix entries. This prevents code replication and allows programmers to work more efficiently. We present the “Iterative Solver Template Library” (ISTL) which is part of the “Distributed and Unified Numerics Environment” (DUNE). It applies generic programming in C++ to the domain of iterative solvers of linear systems stemming from finite element discretizations. Those discretizations exhibit a lot of structure. Our matrix and vector interface supports a block recursive structure. Each sparse matrix entry can itself be either a sparse or a small dense matrix. Based on this interface we present efficient solvers that use the recursive block structure via template metaprogramming.

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  1. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  2. Engwer, Christian; Wenske, Michael: Estimating the extent of glioblastoma invasion. Approximate stationalization of anisotropic advection-diffusion-reaction equations in the context of glioblastoma invasion (2021)
  3. Götschel, Sebastian; Schiela, Anton; Weiser, Martin: Kaskade 7 -- a flexible finite element toolbox (2021)
  4. Koch, Timo; Gläser, Dennis; Weishaupt, Kilian; Ackermann, Sina; Beck, Martin; Becker, Beatrix; Burbulla, Samuel; Class, Holger; Coltman, Edward; Emmert, Simon; Fetzer, Thomas; Grüninger, Christoph; Heck, Katharina; Hommel, Johannes; Kurz, Theresa; Lipp, Melanie; Mohammadi, Farid; Scherrer, Samuel; Schneider, Martin; Seitz, Gabriele; Stadler, Leopold; Utz, Martin; Weinhardt, Felix; Flemisch, Bernd: DuMu(^\textx 3) -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling (2021)
  5. Rasmussen, Atgeirr Flø; Sandve, Tor Harald; Bao, Kai; Lauser, Andreas; Hove, Joakim; Skaflestad, Bård; Klöfkorn, Robert; Blatt, Markus; Rustad, Alf Birger; Sævareid, Ove; Lie, Knut-Andreas; Thune, Andreas: The open porous media flow reservoir simulator (2021)
  6. Beck, M.; Rinaldi, A. P.; Flemisch, B.; Class, H.: Accuracy of fully coupled and sequential approaches for modeling hydro- and geomechanical processes (2020)
  7. Gratien, Jean-Marc: A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores (2020)
  8. Koch, Timo; Schneider, Martin; Helmig, Rainer; Jenny, Patrick: Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources (2020)
  9. Sander, Oliver: DUNE -- the distributed and unified numerics environment (2020)
  10. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  11. Vidotto, Ettore; Koch, Timo; Köppl, Tobias; Helmig, Rainer; Wohlmuth, Barbara: Hybrid models for simulating blood flow in microvascular networks (2019)
  12. Kröner, Axel; Kröner, Eva; Kröner, Heiko: Finite element approximation of level set motion by powers of the mean curvature (2018)
  13. Schmidt, Stephan: Weak and strong form shape hessians and their automatic generation (2018)
  14. Hunt, Alexander; Surulescu, Christina: A multiscale modeling approach to glioma invasion with therapy (2017)
  15. Schneider, Martin; Agélas, Léo; Enchéry, Guillaume; Flemisch, Bernd: Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes (2017)
  16. Schneider, Martin; Gläser, Dennis; Flemisch, Bernd; Helmig, Rainer: Nonlinear finite-volume scheme for complex flow processes on corner-point grids (2017)
  17. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  18. Tobias Leibner, Rene Milk, Felix Schindler: Extending DUNE: The dune-xt modules (2016) arXiv
  19. Efendiev, Yalchin; Kronsbein, Cornelia; Legoll, Frédéric: Multilevel Monte Carlo approaches for numerical homogenization (2015)
  20. Bastian, Peter; Heimann, Felix; Marnach, Sven: Generic implementation of finite element methods in the distributed and unified numerics environment (DUNE) (2010)

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